Boil diced potatoes until just soft. Meanwhile, blanch broccoli in small amount of water. Reduce heat to medium and add cheese and cream. Stir frequently until melted.
Drain potatoes, reserving liquid. Add half of the diced potatoes to the soup and fork mash the other half before adding to soup. Add potato water until desired consistency and richness. Salt and pepper to taste.
Soup may be thickened with 1/2 tsp cornstarch and 1 tsp water.